We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid–solid interaction. The simulations are conducted in a two-dimensional, horizontally periodic domain with an aspect ratio of 4, and the porosity ϕ is varied from 0.7 to 1, while the solute Rayleigh number R a S ranges from 4 × 10 6 to 4 × 10 9. Our results show that, for all explored R a S, solute transport first enhances unexpectedly with decreasing ϕ and then decreases when ϕ is smaller than a R a S-dependent value. On the other hand, while the flow strength decreases significantly as ϕ decreases at low R a S, it varies weakly with decreasing ϕ at high R a S and even increases counterintuitively for some porosities at moderate R a S. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller ϕ and higher R a S. These findings have important implications for passive control of mass/solute transport in engineering applications.
REFERENCES
1.
R. W.
Schmitt
,
J. R.
Ledwell
,
E. T.
Montgomery
et al, “
Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic
,” Science
308
(5722
), 685
–688
(2005
).2.
R. W.
Schmitt
, “
The characteristics of salt fingers in a variety of fluid systems, including stellar interiors, liquid metals, oceans, and magmas
,” Phys. Fluids
26
(9
), 2373
–2377
(1983
).3.
C.
Almarcha
,
Y.
R'Honi
,
Y.
De Decker
et al, “
Convective mixing induced by acid–base reactions
,” J. Phys. Chem. B
115
(32
), 9739
–9744
(2011
).4.
S.
Maruyama
,
T.
Yabuki
,
T.
Sato
et al, “
Evidences of increasing primary production in the ocean by Stommel's perpetual salt fountain
,” Deep Sea Res., Part I
58
(5
), 567
–574
(2011
).5.
D. W. A.
Whitfield
,
G.
Holloway
, and
J. Y.
Holyer
, “
Spectral transform simulations of finite amplitude double-diffusive instabilities in two dimensions
,” J. Mar. Res.
47
(2
), 241
–265
(1989
).6.
C. Y.
Shen
and
G.
Veronis
, “
Numerical simulation of two-dimensional salt fingers
,” J. Geophys. Res.
102
(C10
), 23131
–23143
, https://doi.org/10.1029/97JC01580 (1997
).7.
T. M.
Özgökmen
,
O. E.
Esenkov
, and
D. B.
Olson
, “
A numerical study of layer formation due to fingers in double-diffusive convection in a vertically-bounded domain
,” J. Mar. Res.
56
, 463
–487
(1998
).8.
O. P.
Singh
and
J.
Srinivasan
, “
Effect of Rayleigh numbers on the evolution of double-diffusive salt fingers
,” Phys. Fluids
26
(6
), 062104
(2014
).9.
Y.
Yang
,
R.
Verzicco
, and
D.
Lohse
, “
Vertically bounded double diffusive convection in the finger regime: Comparing no-slip versus free-slip boundary conditions
,” Phys. Rev. Lett.
117
(18
), 184501
(2016
).10.
Y.
Yang
,
R.
Verzicco
, and
D.
Lohse
, “
Scaling laws and flow structures of double diffusive convection in the finger regime
,” J. Fluid Mech.
802
, 667
–689
(2016
).11.
Y.
Yang
,
W.
Chen
,
R.
Verzicco
et al, “
Multiple states and transport properties of double-diffusive convection turbulence
,” Proc. Natl. Acad. Sci. U.S.A.
117
(26
), 14676
–14681
(2020
).12.
M. E.
Stern
and
J. A.
Simeonov
, “
Internal wave overturns produced by salt fingers
,” J. Phys. Oceanogr.
32
(12
), 3638
–3656
(2002
).13.
M.
Dadonau
, The Effect of Double Diffusion on the Dynamics of Turbulent Plumes and Jets
(
University of Cambridge
, 2020
).14.
R.
Ouillon
,
P.
Edel
,
P.
Garaud
et al, “
Settling-driven large-scale instabilities in double-diffusive convection
,” J Fluid Mech.
901
, A12
(2020
).15.
X.
Zhang
,
L. L.
Wang
,
C.
Lin
et al, “
Numerical study on tilting salt finger in a laminar shear flow
,” Phys. Fluids
30
(2
), 022110
(2018
).16.
P.
Garaud
,
A.
Kumar
, and
J.
Sridhar
, “
The interaction between shear and fingering (thermohaline) convection
,” Astrophys. J.
879
(1
), 60
(2019
).17.
J.
Li
and
Y.
Yang
, “
Flow structures and vertical transport in tilting salt fingers with a background shear
,” Phys. Rev. Fluids
7
(5
), 053501
(2022
).18.
T.
Green
, “
Scales for double‐diffusive fingering in porous media
,” Water Resour. Res.
20
(9
), 1225
–1229
, https://doi.org/10.1029/WR020i009p01225 (1984
).19.
T.
Nishimura
and
M.
Kunishige
, “
Velocity fields of salt-finger convection generated during unidirectional binary solidification
,” Proc. Therm. Eng. Conf.
2003
, 289
–290
.20.
M. Y.
Corapcioglu
and
A. L.
Baehr
, “
A compositional multiphase model for groundwater contamination by petroleum products: 1. Theoretical considerations
,” Water Resour. Res.
23
(1
), 191
–200
, https://doi.org/10.1029/WR023i001p00191 (1987
).21.
Y.
Katto
and
T.
Masuoka
, “
Criterion for the onset of convective flow in a fluid in a porous medium
,” Int. J. Heat Mass Transfer
10
(3
), 297
–309
(1967
).22.
J. W.
Taunton
,
E. N.
Lightfoot
, and
T.
Green
, “
Thermohaline instability and salt fingers in a porous medium
,” Phys. Fluids
15
(5
), 748
–753
(1972
).23.
P. T.
Imhoff
and
T.
Green
, “
Experimental investigation of double-diffusive groundwater fingers
,” J. Fluid Mech.
188
, 363
–382
(1988
).24.
J.
Taylor
and
G.
Veronis
, “
Experiments on salt fingers in a Hele Shaw cell
,” Science
231
(4733
), 39
–41
(1986
).25.
C. A.
Cooper
,
R. J.
Glass
, and
S. W.
Tyler
, “
Effect of buoyancy ratio on the development of double‐diffusive finger convection in a Hele‐Shaw cell
,” Water Resour. Res.
37
(9
), 2323
–2332
, https://doi.org/10.1029/2001WR000343 (2001
).26.
C. L.
Werner
, “
Double-diffusive fingering in porous media
,” Ph.D. dissertation (Florida State University, 2017
).27.
P. A.
Tyvand
, “
Thermohaline instability in anisotropie porous media
,” Water Resour. Res.
16
(2), 325
–330
, https://doi.org/10.1029/WR016i002p00325 (1980).28.
B. T.
Murray
, “
Experimental and numerical investigation of double-diffusive convection in a horizontal layer of porous medium
,” Ph.D. thesis (
University of Arizona
, 1986
).29.
Y. Y.
Luo
,
J. M.
Zhan
, and
Y. S.
Li
, “
Numerical simulation of salt finger convection in porous media
,” Acta Phys. Sin.
57
(4
), 2306
–2313
(2008
).30.
M.
Firdaouss
,
J. L.
Guermond
, and
P.
Le Quéré
, “
Nonlinear corrections to Darcy's law at low Reynolds numbers
,” J. Fluid Mech.
343
, 331
–350
(1997
).31.
F.
Ahmad
,
A.
Rahimi
,
E.
Tsotsas
et al, “
From micro-scale to macro-scale modeling of solute transport in drying capillary porous media
,” Int. J. Heat Mass Transfer
165
, 120722
(2021
).32.
F.
Chen
and
C. F.
Chen
, “
Double-diffusive fingering convection in a porous medium
,” Int. J. Heat Mass Transfer
36
(3
), 793
–807
(1993
).33.
B. D.
Wood
,
X.
He
, and
S. V.
Apte
, “
Modeling turbulent flows in porous media
,” Annu. Rev. Fluid Mech.
52
, 171
–203
(2020
).34.
Y.
Chen
,
G.
Jin
,
P.
Zhang
et al, “
Intercomparison of boundary schemes in lattice Boltzmann method for flow simulation in porous media
,” Int. J. Numer. Methods Fluids
92
(12
), 2009
–2029
(2020
).35.
Z.
Wang
,
L.
Chen
,
H.
Wei
et al, “
Pore-scale study of mineral dissolution in heterogeneous structures and deep learning prediction of permeability
,” Phys. Fluids
34
(11
), 116609
(2022
).36.
L.
Ju
,
B.
Shan
,
P.
Liu
et al, “
Pore-scale study of miscible density-driven mixing flow in porous media
,” Phys. Fluids
33
(3
), 034113
(2021
).37.
Q.
Gu
,
L.
Zhu
,
Y.
Zhang
et al, “
Pore-scale study of counter-current imbibition in strongly water-wet fractured porous media using lattice Boltzmann method
,” Phys. Fluids
31
(8
), 086602
(2019
).38.
D.
Panda
,
S.
Paliwal
,
D. P.
Sourya
et al, “
Influence of thermal gradients on the invasion patterns during drying of porous media: A lattice Boltzmann method
,” Phys. Fluids
32
(12
), 122116
(2020
).39.
X.
Zhang
,
L.
Wang
,
H.
Zhu
et al, “
Pore-scale simulation of salt fingers in porous media using a coupled iterative source-correction immersed boundary-lattice Boltzmann solver
,” Appl. Math. Modell.
94
, 656
–675
(2021
).40.
S.
Liu
,
L.
Jiang
,
K. L.
Chong
et al, “
From Rayleigh–Bénard convection to porous-media convection: How porosity affects heat transfer and flow structure
,” J. Fluid Mech.
895
, A18
(2020
).41.
J.
Yoshida
and
H.
Nagashima
, “
Numerical experiments on salt-finger convection
,” Prog. Oceanogr.
56
(3–4
), 435
–459
(2003
).42.
M. E.
Stern
, “
Three-dimensional salt fingers in an unbounded thermocline
,” J. Mar. Res.
59
, 355
–390
(2001
).43.
Y.
Yang
et al, “
Layering and vertical transport in sheared double-diffusive convection in the diffusive regime
,” J. Fluid Mech.
933
, A30
(2022
).44.
Y.
Han
and
P. A.
Cundall
, “
Lattice Boltzmann modeling of pore‐scale fluid flow through idealized porous media
,” Int. J. Numer. Methods Fluids
67
(11
), 1720
–1734
(2011
).45.
H.
Khozeymeh-Nezhad
and
H.
Niazmand
, “
A double MRT-LBM for simulation of mixing in an active micromixer with rotationally oscillating stirrer in high Peclet number flows
,” Int. J. Heat Mass Transfer
122
, 913
–921
(2018
).46.
Y.
Yang
, “
Double diffusive convection in the finger regime for different Prandtl and Schmidt numbers
,” Acta Mech. Sin.
36
(4
), 797
–804
(2020
).47.
S. D.
Huang
,
M.
Kaczorowski
,
R.
Ni
et al, “
Confinement-induced heat-transport enhancement in turbulent thermal convection
,” Phys. Rev. Lett.
111
(10
), 104501
(2013
).48.
J. Q.
Zhong
,
R. J. A. M.
Stevens
,
H. J. H.
Clercx
et al, “
Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Bénard convection
,” Phys. Rev. Lett.
102
(4
), 044502
(2009
).49.
Y. B.
Hu
,
S. D.
Huang
,
Y. C.
Xie
et al, “
Centrifugal-force-induced flow bifurcations in turbulent thermal convection
,” Phys. Rev. Lett.
127
(24
), 244501
(2021
).50.
K. L.
Chong
,
Y.
Yang
,
S. D.
Huang
et al, “
Confined Rayleigh-Bénard, rotating Rayleigh-Bénard, and double diffusive convection: A unifying view on turbulent transport enhancement through coherent structure manipulation
,” Phys. Rev. Lett.
119
(6
), 064501
(2017
).51.
F.
Wang
,
S. D.
Huang
, and
K. Q.
Xia
, “
Contribution of surface thermal forcing to mixing in the ocean
,” J. Geophys. Res.: Oceans
123
(2
), 855
–863
, https://doi.org/10.1002/2017JC013578 (2018
).52.
F.
Wang
,
S. D.
Huang
,
S. Q.
Zhou
et al, “
Laboratory simulation of the geothermal heating effects on ocean overturning circulation
,” J. Geophys. Res.: Oceans
121
(10
), 7589
–7598
, https://doi.org/10.1002/2016JC012068 (2016
).53.
A.
Rosenthal
,
K.
Lüdemann
, and
A.
Tilgner
, “
Staircase formation in unstably stratified double diffusive finger convection
,” Phys. Fluids
34
(11
), 116605
(2022
).54.
S.
Garai
and
S.
Sahoo
, “
On convective instabilities in a rotating fluid with stably stratified layer and thermally heterogeneous boundary
,” Phys. Fluids
34
(12
), 124101
(2022
).55.
M.
Singh
et al, “
Predicting the effect of inertia, rotation, and magnetic field on the onset of convection in a bidispersive porous medium using machine learning techniques
,” Phys. Fluids
35
(3
), 034103
(2023
).56.
K. Q.
Xia
,
S. D.
Huang
,
Y. C.
Xie
et al, “
Tuning heat transport via coherent structure manipulation: Recent advances in thermal turbulence
,” Natl. Sci. Rev.
10
, nwad012
(2023
).57.
G.
Kefayati
, “
Lattice Boltzmann simulation of double-diffusive natural convection of viscoplastic fluids in a porous cavity
,” Phys. Fluids
31
(1
), 013105
(2019
).58.
G.
Kefayati
et al, “
A mesoscopic model for thermal–solutal problems of power-law fluids through porous media
,” Phys. Fluids
33
(3
), 033114
(2021
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
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